The Advising & Learning Centers
Ciletti Memorial Library, Lower Level
570-385-6140
Academic Skills for the Sciences
Biology
Chemistry
Physics
2
There are no tricks or magic “formulas” for succeeding in science, but this handout does offer
practical suggestions to improve your academic skills specifically for science courses. The following
academic skill strategies are meant to be used in addition to general academic skills which are
outlined in our other skills handouts located in the CAA lobby.
The following science skills strategies have been separated into three sections: Biology, Chemistry,
and Physics each offering specific suggestions for that discipline. However, most of the strategies can
be applied to any science.
I.
Biology
A. Reading Skills
1.
Read slowly and deliberately. Most college biology texts are at least a 12.6 grade level
and some are higher. The reading flow is not like the flow of a novel, effortless and
rapid. When you are not concentrating on the text reading you will get very little out of
it and it will seem more difficult than it really is.
2.
Tackle it three times. Yes, this sounds like a lot, but if you put quality time and effort
into it at the beginning it will take a lesser quantity of time and effort later.
a.
First: skim the chapter, noting topic sentences, words in bold, all tables, diagrams,
and summary charts. This should be done before the lecture.
a.
Second: Read in more detail, studying each area and not proceeding until each
section is understood. Reread as many times as necessary until you understand. If
you are having difficulty, write a specific question about it to ask the instructor.
c.
Third: Go back over the reading to write down terms, definitions, and important
concepts. It is helpful for later in-class note-taking to make a list of key words and
names at this time.
3.
Talk to yourself as you read. Explain what you have read aloud, making up your own
examples to better understand what you have read. Pretend you are explaining the
material to a twelve year old. This will help you clarify the information. Hearing yourself
really makes a difference!
4.
Words and symbols have specific meanings. Each time you come across a new term or
concept, write it down. Whenever possible write it in your own words. Strive for
understanding the definitions so that you can easily restate them. Remember to talk to
yourself out loud.
5.
Study all diagrams and charts. They condense a lot of important information. After
studying, cover the diagram/chart up and rewrite it.
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6.
B.
Use your text. You paid for it!
a.
Highlight important facts and key concepts.
a.
Summarize concepts in your own words in the margins.
c.
Note questions that you need clarified.
7.
Mastery. Make sure you can answer the study questions at the end of the chapters.
8.
Remember to use the reading skills strategies given in the “Study Skills” handout. Those
strategies are the base to add any discipline specific skills to. But of course you’re
already using them!
Study Skills:
1.
Biology utilizes a large amount of information that a student must master and
memorize.
a.
Re-Organize. Below are some strategies to reorganize lecture, lab, and text
material in meaningful ways for more effective studying by reducing the amount of
information that must be learned and remembered. Another benefit of
reorganization is that it forces students to use and think about information in
different ways, helping students to detect patterns, predict possible test questions,
and acting as memory triggers. This strategy is extremely important for visual
learners.
b.
Flash Cards are used to organize information such as terms and definitions, people
and their contributions, lists, identifying characteristics, and structures. To get
started using flash cards, use the bold words or main concepts listed in your text.
Genotype
Genetic composition of an
individual
Front
Back
Inheritance of acquired traits
Lamarch
Front
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ex. Giraffe necks grew long to fulfill
need to reach high branches;
longer neck trait then passed to
offspring
Back
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Kingdom
Phylum
Class
Order
Family
Genus
Species
Back
Linnean system
Front
-boundary of all cells
Cell membrane
-made up mostly of phospholipids
and proteins
-controls exit and entry into cells
Front
c.
Back
Matrices are used to show comparisons between two or more concepts (similarities
and differences). Matrices require one to make a connection between different
components; the more connections you make, the more likely you are to remember
the material. Information is organized into rows and columns, with the objects to
be compared written across the top as column headings and the repeating
categories written down the left-hand side row headings.
IMMATURE AND MATURE ECOSYSTEMS
Plant Size
Species Diversity
Immature
Small
Mature
Large
Low
High
Niches
Few, Generalized
Many, Specialized
Organization
Low
High
Energy Efficiency
Low
High
Low
High
Trophic Structure Types
Nutrient Recycling
Matrix from: http://muskingum.edu/~cal/database/content/biology.html
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d.
Concept Maps are used to organize supporting information related to one topic.
They help to organize large chunks of related information. Research supports the
effectiveness of this strategy in helping students learn complex material. For
detailed information on making concept maps, check out these web sites:
http://www.coun.uvic.ca
http://classes.aces.uiuc.edu/
Map from: http://www.inspiration.com/visual-learning
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a.
Hierarchical Organizers show superordinate and subordinate relationships. When
reviewing notes, look for clue words that indicate the information might be
hierarchical: characteristics of/for…, styles of…, types of….
The Linnean Taxonomic Hierarchy







Imperium ("Empire") - the phenomenal world
Regnum ("Kingdom") - the three great divisions of nature at the time - animal,
vegetable, and mineral
Classis ("Class") - subdivisions of the above, in the animal kingdom six were
recognized (mammals, birds, amphibians, fish, insects, and worms)
Ordo ("Order") - further subdivision of the above - the class Mammalia has eight
Genus - further subdivisions of the order - in the mammalian order Primates there
are four. e.g. Homo
Species - subdivisions of genus, e.g. Homo sapiens.
Varietas ("Variety") - species variant, e.g. Homo sapiens europaeus.
Example take from: http://palaeos.com/
For further information and organizer templates, check out this website:
http://www.myschoolonline.com/content_gallery/0,3138,55356-121175-5-5622,00.html
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B.
Memory Strategies are designed to improve encoding and retrieval of information to and
from memory. For biology classes, it is extremely important to begin the memorization
process early so the large amounts of information can be in the long-term memory.
1.
Mnemonics are verbal devices which help one remember a large quantity of facts. The
first letter of each item is used to form a catchy cue word or phrase. Mnemonics are
especially helpful for audio learners.
a.
Create an acronym: Use the first letter of each item to create an easy to remember
word.
To remember types of bacterial flagella:
LAMP




Lophotrichous
Amphitrichous
Monotrichous
Peritrichous
b.
Create an acrostic: Make a sentence using words that have the same first letter as
the items you need to remember.
c.
Mnemonic for remembering planets
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Mercury
My
Venus
Very
Earth
Easy
Mars
Method
Jupiter
Just
Saturn
Speeds
Uranus
Up
Neptune
Naming
Pluto
Planets
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d.
Alphabetizing: Often simply alphabetizing a long list will make recall easier. For
example, arranging the names of the major systems of the body in alphabetical
order forms a list with two consecutive letter combinations, “c-d-e” and “l-m-n”,
plus “r”.
1) Circulatory
2) Digestive
3) Endocrine
4) Excretory
5) Lymphatic
6) Musculoskeletal
7) Nervous
8) Reproductive
9) Respiratory
e.
What to study?
1) Anything mentioned in lecture or lab
2) The more time that is spent on a topic, the more time you should spend
studying it.
3) The more places something is mentioned, the more important it is (lecture, lab,
text.)
4) Be able to define terms and symbols used by instructor.
5) Learn the content of figures used to illustrate concepts, principle, processes,
and facts.
6) Items missed by many students on a quiz or previous test may reappear on the
next test.
7) If it’s important enough for your instructor to repeat it, you better know it!
8) Problems solved in lab, lecture, or recitation are a sample of what to expect.
Practice them so you can solve similar problems.
9) Hints from instructor.
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C.
Test taking
1.
Information Dumping: As soon as you get the test, dump all of the information you
think you might forget or confuse while taking the test. On the back of the test or on
scrap paper provided by the instructor, write down numerical data, names, figures,
drawings, mnemonics, or organizational schemes. It is worth the time it takes to dump
the information to ensure that you don’t forget it.
2.
See “Test-taking Strategies” handout for important test-taking tips.
D. Lab Strategies
II.
1.
Preparation: Read the procedure before class and prepare a
“summarized lab procedure” by writing a shortened, step-by-step version of what you
will be doing. Eliminate all extraneous words and explanations. If during lab something
isn’t clear, you can refer to your lab manual for clarification.
2.
Slide Identification: Some lab tests require identification of slides (cell, cell structures,
species, or parts of the anatomy). Flash cards are an effective tool. First, photo copy
the diagram or picture from your lab book (you may need to reduce the size). Use white
out to cover over any identifying terms on the diagram. Cut out and attach the new
picture to one side of an index card. Identify the picture on the back of the card.
3.
Keep a separate binder or binder section for lab materials. A three-ring binder is best as
handouts may be added easily.
Chemistry
A. The above biology strategies also apply to chemistry. In addition to those strategies, be
aware that chemistry is cumulative as it progresses from simple to complex, building upon
existing knowledge at each stage. New work may only be understood after earlier work has
been well understood. Therefore, be very careful to keep up with work and not fall behind.
Sometimes chemistry does not follow a nice logical sequence like most other subjects. You
may have to accept some things as fact without being able to see all the processes at first.
B.
Basics needed to succeed in chemistry:
1.
Simple algebra
2.
Metric system (length, mass, volume)
3.
Significant numbers
4.
Temperature (Fahrenheit, Celsius, Kelvin)
5.
Exponential numbers
6.
Factor-label method (dimensional analysis
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C.
7.
Chemical symbols and names of about 40 commonly used elements
8.
Symbols (formulas) and names of commonly used ions
9.
Writing and naming chemical formulas
Five traditional branches of chemistry: Your chemistry course may include any combination
of the five branches. Understanding the focus of each branch of chemistry will help you
better understand the concepts you are learning in a particular branch.
1.
Inorganic chemistry studies the structure and chemical reactions of substances
composed of any of the known elements, except carbon-containing substance.
2.
Organic chemistry studies the compounds of carbon.
3.
Physical chemistry or theoretical chemistry applies the application of theories and
mathematical methods to the solution of chemical problems.
4.
Analytical chemistry deals with two areas: qualitative analysis (qual), “What is there?”
and quantitative analysis (quant), “How much is there?”
5.
Biochemistry (physiological chemistry) studies the chemical structure of living material
and the chemical reactions occurring in living cells.
6.
General chemistry gives you an overview of each of the branches.
D. Reading – see “reading” section under biology in this handout.
E.
Study Skills
1.
Basics
a.
As mentioned earlier, it is extremely important to know the basics in chemistry. For
example, most of the more complex topics in chemistry revolve around the topics
of chemical bonding, nomenclature, and atomic structure. It is difficult to picture
what is happening with Nitric Acid if you don’t know it is H 2NO3. It is difficult to
picture how ions are formed, if you don’t know the basic atomic structure. Spend a
lot of time studying and understanding the basics to make the rest of your
chemistry go smoother.
b.
It is important to know the difference between an abbreviation and a symbol. An
abbreviation is just the shortened form of a word, but a symbol can have many
meanings and you may need to know all of those meaning.
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2.
Terminology and symbols: Learning these are one of the most important things to do!
a.
Write out all the definitions in your own words and gives examples where helpful.
Recite the definitions. Do the same with the symbols. The “flashcard” method
works wonders with these (see “flashcards” in the biology section).
b.
Use every opportunity as a mini quiz. For example, when reading your text,
reviewing notes, or whenever you come across chemical substances, recite their
symbol or chemical formula.
TIP→ Check out some of the ingredient labels on products at home or in the grocery
store and see if you can recognize the common and formal name. For example, “Tums”
is calcium carbonate, and rubbing alcohol is isopropyl alcohol. What is their formula?
c.
Keep a running list of chemical substances and their symbols or formulas. It is also
helpful to note any descriptive factors. You can use a matrix to organize the
information! (see “matrices” in the biology section.)
d.
Make problem solving a part of every study session. Decide on a number of
problems to work out at every study session and do them! Your proficiency in
solving problems will increase with practice. If you find the problems to be difficult
at first, practice by using the problems worked out in the text. Cover up the
solutions in your text and then work out the problems. If you get stuck, take a look
at the solution to help you figure it out. It is extremely helpful to work problems
with a study partner, you can help each other when needed. It’s often said that the
number one reason whey students fail chemistry is that they do not work enough
problems!
e.
Become one with the Periodic Table! Learn how to use it and keep a copy of it
easily accessible.
Check out these web-sites for interaction periodic tables and table information.



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http://www.webelements.com/
http://www.bc.edu/schools/cas/chemistry/
http://www.funbrain.com/periodic/index.html (learning tool)
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III. Physics
A. It is important to be aware that physics is a problem-solving discipline. Your instructor will
stress major themes and principles, but the one major goal is that you, the student, will be
able to apply these principles to understand and solve problems.
B.
C.
Reading
1.
In physics, reading the text and solving homework problems is a cycle: Questions lead
to answers which lead back to more questions. An entire chapter will often be devoted
to the consequences of a single basic principle. You should look for the basic principles.
Understanding these Laws of Nature will help you see the order to the physicists' view
of the universe. Nearly all of the problems that you will be faced with in a physics
course can be analyzed by means of one or more of these laws.
2.
Be sure to review the reading tips in the biology section of this handout and the general
study skill handout.
Problem Solving
1.
Effective problem solving involves answering seven questions:
a. What's the problem about?
b. What am I asked to find?
c. What information am I to use?
d. What principles apply?
e. What do I know about similar situations?
f.
How can I go about applying the information to solve the problem?
g. Does my solution make sense?
2.
Most effective approach:
a.
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An effective problem solver will decide, "this is an energy problem," or, "this is a
Newton 2 problem." An inexperienced problem solver is more likely to decide, "this
is a pulley problem," or, "this is a baseball problem." The inexperienced solver
concentrates on the surface features of the problem while it is more effective to
concentrate on the underlying principle. The expert problem solver, will answer
these questions, play around (briefly) with the problem, and make drawings and
sketches (either in the mind, or even better, on paper) before writing down
formulas and plugging in numbers. An inexperienced solver, on the other hand, will
try to write down equations and plug in numbers as soon as possible, making more
mistakes and taking more time.
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3.
4.
Physics insight:
a.
In a physics course it's important to remember a couple of
things about physic. A physicist seeks those problems that can
be modeled or represented by a picture or a diagram. Almost
any problem you encounter in a physics course can be
described with a drawing. Such a drawing often contains or
suggests the solution to the problem.
b.
A physicist seeks to find unifying principles that can be expressed mathematically
and that can be applied to broad classes of physical situations. Your physics
textbook contains many specific formulas, but you must understand the broader
Laws of Nature in order to grasp the general overview of physics. This broad
understanding is vital if you are to solve problems that may include several different
principles and that may use several different formulas. Virtually all specific formulas
in physics are combinations of basic laws.
General outline of problem solving approach:
a.
Read the problem. Look up meanings of any terms you’re not sure about. Ask
yourself, “What is this about?” Express the problem in your own words.
b.
Make a drawing of the problem. Generally, a rough drawing is all that is needed,
but if a more effective drawing is needed, include the following:
1) A title that identifies the quantity you are seeking in the problem.
2) Label the drawing, including the parameters or variables on which the solution
depends and that are given in the problem. Make sure to include the given
values.
3) Label any unknown parameters that must be calculated or obtained in order to
find the solution.
4) Be sure to use the units of measure for all quantities in the problem.
5) Include information that is assumed (such as g, the value of the acceleration
due to gravity), and whether air resistance and friction are neglected.
c.
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Establish which general principle relates the given parameters of the quantity that
you are seeking. Usually your drawing will suggest the techniques and formulas to
be used. Sometimes it may be necessary to obtain further information from your
text or notes before the right formulas can be determined. Often further
information is needed when the problem has a solution that must be calculated
indirectly from the given information. If further information is needed or if
intermediate quantities must be computed, it is here that they are often identified.
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d.
Draw a second picture that identifies the coordinate system and origin that will be
used in relating the data to the equations. In some situations this second picture
may be a graph, free body diagram, or vector diagram rather than a picture of a
physical situation.
1) Vector diagrams are diagrams which depict the
direction and relative magnitude of a vector
quantity by a vector arrow. Vector diagrams can
be used to describe the velocity of a moving
object during its motion. For example, the velocity
of a car moving down the road could be
represented by a vector diagram.
2) Free-body diagrams are diagrams used to show the relative magnitude and
direction of all forces acting upon an object in a given situation. A free-body
diagram is a special example of the vector diagrams
a)
Graph: Depicts the position and time for a moving car.
Leftward (–) Velocity;
Fast to Slow
e.
Leftward (–) Velocity;
Slow to Fast
Problem working methods:
1) In the Concrete method calculation is done using the given values from the
start, so that the algebra gives numerical values at each intermediate step on
the way to the final solution. The disadvantage of this method is that because
of the large number of numerical calculations involved, mistakes are likely, and
so you should take special care with significant figures. However this method
has the advantage that you can see, at every step of the way, how the problem
is progressing. It also is more direct and often makes it easier to locate a
mistake if you do make one.
2) In the formal method you calculate the solution by doing as much as possible
without using specific numbers. In other words, do as much of the algebra as
you can before substituting the specific given values of the data. In long and
complicated problems terms may cancel or expressions simplify.
3) TIP →Gain experience in problem solving by substituting the numbers when
you start physics, but gradually adopt the formal approach as you become
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more confident; many people adopt a compromise approach where they
substitute some values but retain others as symbols (for example, "g" for the
acceleration due to gravity).
f.
Criticize your solution. Ask yourself, “Does this make sense?” Compare your
solution to any available examples or to previous problems you have done. Often
you can check yourself by doing an approximate calculation. Many times a
calculation error will result in an answer that is obviously wrong. Be sure to check
the units of your solution to see that they are appropriate. This examination will
develop your physical intuition about the correctness of solutions, and this intuition
will be very valuable for later problems and on exams.
TIP: An important thing to remember in working physics problems is that by showing all of your work
you can more easily locate and correct mistakes. You will also find it easier to study the problems
when preparing for exams if you show all your work. Also, practice doing the problem faster when
studying. This will help you build up your speed and confidence for exam time.
g.
Examples applying Problems-Solving Principles: In the following examples,
problems are stated and the solution is written down as you would work it out for
homework.
h.
Example #1: In 1947, Bob Feller, former Cleveland pitcher, threw a baseball across
the plate at 98.6 mph or 44.1 m/s. For many years this was the fastest pitch ever
measured. If Bob had thrown the pitch straight up, how high would it have gone?
1) What does the problem ask for, and what is given? Answer: The speed of the
baseball is given, and what is wanted is the height that the ball would reach if it
were thrown straight up with the given initial speed. You should double check
that whoever wrote the problem correctly calculated that 98.6 miles/hr is
equal to 44.1 m/s. You should state explicitly, in words, that you will use the
44.1 m/s figure and that you will assume the baseball is thrown from an initial
height of zero (ground level). You should also state explicitly what value of g
you will use, for example, g = 9.81 m/s2. You should also state that you assume
that air resistance can be neglected. Since you don't know the mass of the
baseball, say that you don't (you won't need it, anyway).
2) Make a drawing:
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3) The general principles to be applied here are those of uniformly accelerated
motion. In this case, the initial velocity vo decreases linearly in time because of
the gravitational acceleration. The maximum height ym occurs at the time tm
when the velocity reaches zero. The average velocity during from t = 0 to t = t m
is the average of the initial velocity v = vo and the final velocity v = 0, or half the
initial velocity.
4) Make a second drawing. In this case, try a graph of velocity as a function of
time:
Notice that the graph is fairly accurate: You can approximate the value of g as 10 m/s 2, so that the
velocity decreases to zero in about 4.5 s. Therefore, even before you use your calculator, you have a
good idea of about the value of tm.
5) The concrete method can now be applied: An initial velocity of 44.1 m/s will
decrease at the rate of 9.81 m/s2 to zero in a time tm given by
a)
tm = 44.1 / 9.81 = 4.4954 s .
b) During that time, the average velocity is vav = 44.1 / 2 = 22.05 m/s.
Therefore the height is given by
c)
ym = vav tm = 99.12 = 99.1 m .
Notice that for all "internal" calculations, more than the correct number of significant figures were
kept; only when the final answer was obtained was it put into the correct number of significant
figures, in this case three.
6) To do this problem in a formal method, use the formula for distance y as a
function of t if the acceleration a is constant. Do not substitute numbers, but
work only with symbols until the very end:
a)
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y = yo + vo t + a t2 / 2 ,
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b) where yo = 0 is the initial position, vo = 44.1 m/s is the initial velocity, and a
= - g = - 9.81 m/s2 is the constant acceleration. However, do not use the
numerical figures at this point in the calculation. The maximum value of y
is when its derivative is zero; the time tm of zero derivative is given by:
c)
dy/dt = vo + a tm = 0 --> tm = - vo / a .
d) The maximum height ym is given by putting this value of tm into the
equation for y:
e) ym = yo + vo ( - vo / a ) + a ( - vo / a )2 / 2 = yo - vo2 / 2a .
f)
Now substitute: yo = 0, vo = 44.1, a = - 9.81. The result is
g)
ym = 0 + 0.5 (44.1)2 / 9.81 = 99.1 m .
7) Look over this problem and ask yourself if the answer makes sense. After all,
throwing a ball almost 100 m in the air is basically impossible in practice, but
Bob Feller did have a very fast, fast ball pitch!
a)
There is another matter: If this same problem had been given in a chapter
dealing with conservation of energy, you should not solve it as outlined
above. Instead, you should calculate what the initial and final kinetic
energy KE and potential energy PE are in order to find the total energy.
Here, the initial PE is zero, and the initial KE is m vo2 / 2. The final PE is m g
ym and the final KE is zero. Equate the initial KE to the final PE to see that
the unknown mass m cancels from both sides of the equation. You can
then solve for ym, and of course you will get the same answer as before but
in a more sophisticated manner.
8) To prepare for an exam, look over this problem and ask yourself how you can
solve it as quickly as possible. You may be more comfortable with the concrete
approach or with the formal approach; practice will tell. On an actual exam,
you might not have time for a complete drawing or a complete listing of
principles. By working this problem a couple of times, even after you've gotten
the answer once, you will become very familiar with it. Even better, explain the
problem to a friend of yours, and that way you really will have it!
a)
Example #2: A one kilogram block rests on a plane inclined at 27 o to the
horizontal. The coefficient of friction between the block and the plane is
0.19. Find the acceleration of the block down the plane.

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The problem asks for the acceleration, not the position of the block nor
how long it takes to go down the plane nor anything else. No mention is
made of the difference between static or kinetic coefficients of friction,
so assume they are the same. The mass is given, but you will eventually
find that it doesn't matter what the mass is. (If the mass had not been
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given, that would be an indication that it doesn't matter, but even in
that case you may find it easier to assume a value for the mass in order
to guide your thoughts as you do the problem.)

Here is the first picture. Note that the angle is labeled , and the
coefficient of friction is labeled . In addition, the use of m for the mass
and a|| for the acceleration down the plane are defined in the picture.

There are two general principles that apply here. The first is Newton's
Second Law:

F=ma,

where F is the net force, a vector, and a is acceleration, another vector;
the two vectors are in the same direction. The mass m will eventually be
found not to make any difference, and in that case, you might be
tempted to write this law as a = F / m, since a is what you want to find.
However, the easiest way to remember Newton's Second Law is F = m a,
and so that is the law to work with.

The second principle is that the frictional force is proportional to the
normal force (the component of the force on the block due to the plane
that is perpendicular to the plane). The frictional force is along the
plane and always opposes the motion. Since the block is initially at rest
but will accelerate down the plane, the frictional force will be up along
the plane. The coefficient of friction, which is used in this
proportionality relation, is .
9) It is now time to draw the second picture. It helps to redraw the first picture
and add information to it. In this case a vector diagram is drawn and various
forces are defined.
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5.
Note that in the vector diagram, the block has been replaced by a dot at the center of
the vectors. The relevant forces are drawn in (all except the net force). Even the value
assumed for the gravitational acceleration has been included. Some effort has been
made to draw them to scale: The normal force is drawn equal in magnitude and
opposite in direction to the component of the gravity force that is perpendicular to the
plane. Also, the friction force has been drawn in parallel to the plane and opposing the
motion; it has been drawn in smaller than the normal force. The angles of the normal
and parallel forces have been carefully drawn in relation to the inclined plane. This subdrawing has a title and labels, as all drawings should.
6.
We will do this problem using the formal approach, leaving the concrete method for a
check (see below).
7.
Now for calculation using the formal approach, where you work with algebra and
symbols rather than with numbers. First state in words what you are doing, and then
write down the equation:
a.
Magnitude of gravity force = weight = m g.
b.
Resolve gravity force into normal component and parallel component whose
magnitudes are:
1) FG|| = m g sin and FGN = m g cos .
c.
The magnitude of the normal force due to the plane is equal in magnitude (but the
direction is opposite) to the magnitude of the normal component of the gravity
force:
1) FN = m g cos .
d.
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The frictional force opposes the motion, and its magnitude is equal to the
coefficient of friction times the normal plane force:
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20
1) Ff = m g cos .
e.
The net force (which is along the plane) is the difference between the parallel
component of the gravitational force and the friction force; its magnitude is:
1) F = m g sin - m g cos .
f.
The acceleration is net force over mass:
1) a|| = g sin - g cos = g ( sin - cos ) .
g.
The numerical answer is (given to two significant figures since the given numbers
have two):
1) a = (9.8 m/s2) (sin 27o - 0.19 cos 27o) = (9.8) (0.454 - 0.19 x 0.891) = 2.79 = 2.8
m/s2 .
8.
When you look over this answer to see if it makes sense, try doing the problem by
substituting numbers in at each step (the concrete approach). The weight of a kilogram,
for example is 9.8 N. The normal (perpendicular to the plane) component of the
gravitational force is 9.8 times cos 27o or 8.73 N. This makes sense, for if the angle were
very small, the normal component of the gravitational force would be almost equal to
9.8 itself. Notice that although the final answer should be given to two significant
figures, you should keep three in these intermediate calculations.
a.
9.
The parallel component of the gravitational force is 9.8 sin 27o = 4.45 N. The normal
force due to the plane is equal in magnitude to the gravitational normal force (but
opposite in direction), and so the frictional force is 0.19 times 8.73 or 1.66 N. The
net force is down the plane and equal to the difference 4.45 - 1.66 = 2.79 N. Divide
this value by 1 kg to get the acceleration 2.79 m/s2 (which is rounded off to 2.8
m/s2).
Again examine your solution. It says that the block does accelerate down the plane
because the final answer is positive. The acceleration is less than g, again a reasonable
result. Notice that if the angle were more than 27 o, then its sine would be larger and its
cosine smaller, so the acceleration would be greater. If the angle were less than 27 o
then the opposite would be true, and the acceleration, as calculated above, could
become negative. But a negative value for acceleration would be wrong, because that
would say that the block would accelerate up the plane because the frictional force
dominates, and that is impossible. Instead, if the calculation had produced a negative
value for a, you would have had to change the solution to a = 0, meaning that the
frictional force was enough to prevent sliding.
D. Now anticipate how you'd do this problem on an exam. Is the concrete approach faster and
easier for you? Or would you be more comfortable using the formal approach on an exam? It
is a good idea to practice doing this problem when you study for an exam, if you think a
similar problem will be asked.
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21
1.
. Memory Strategies and Test-taking: see the biology section of this handout and be
sure to pick up the general study skills and test-taking skill handouts.
Information for this handout was taken from the following web-site sources:
http://apphysicsb.homestead.com/study.html
http://www.heptune.com/passchem.html
http://muskingum.edu/~cal/database/content/biology.html
http://www.physicsclassroom.com/Class/1DKin/U1L3a.cfm
http://pima.edu/campuses-centers/west-campus/index.html
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